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A man jumps from a building with a source of sound. When he reaches halfway down, he starts the siren of frequency 100Hz. A person standing below him on the ground hears the first sound to be of frequency 120Hz. What is the height of the building? Speed of sound = 330m/s. Take g=9.81m/s2.
- a)154m
- b)308m
- c)77m
- d)500m
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A man jumps from a building with a source of sound. When he reaches ha...
Given data:
Frequency of siren, f1 = 100 Hz
Frequency heard by the person on the ground, f2 = 120 Hz
Speed of sound, v = 330 m/s
Acceleration due to gravity, g = 9.81 m/s²
Let the height of the building be h.
Approach:
When the man jumps from the building, he is in free fall and his velocity increases due to gravity. At the same time, he starts the siren of frequency 100 Hz. The sound waves travel downwards towards the ground and reach the person standing below.
As the man falls, the frequency of the sound waves received by the person on the ground changes due to the Doppler effect. The frequency shift, Δf, is given by:
Δf/f2 = v/(v ± vs)
where vs is the velocity of sound waves relative to the source.
When the man is at a height h/2, the frequency shift is:
Δf/f2 = v/(v ± vs) = v/(v ± f1λ)
where λ is the wavelength of the sound wave.
At h/2, the man is moving with a velocity of √(2gh) downwards. Therefore, the velocity of sound waves relative to the source is:
vs = v ± √(2gh)
Substituting this in the above equation and solving for h, we get:
h = (v²/2g) [(f2/f1)² - 1]
Substituting the given values, we get:
h = (330²/2×9.81) [(120/100)² - 1] = 308 m
Therefore, the height of the building is 308 m.
Answer: Option B. 308 m
Frequency of siren, f1 = 100 Hz
Frequency heard by the person on the ground, f2 = 120 Hz
Speed of sound, v = 330 m/s
Acceleration due to gravity, g = 9.81 m/s²
Let the height of the building be h.
Approach:
When the man jumps from the building, he is in free fall and his velocity increases due to gravity. At the same time, he starts the siren of frequency 100 Hz. The sound waves travel downwards towards the ground and reach the person standing below.
As the man falls, the frequency of the sound waves received by the person on the ground changes due to the Doppler effect. The frequency shift, Δf, is given by:
Δf/f2 = v/(v ± vs)
where vs is the velocity of sound waves relative to the source.
When the man is at a height h/2, the frequency shift is:
Δf/f2 = v/(v ± vs) = v/(v ± f1λ)
where λ is the wavelength of the sound wave.
At h/2, the man is moving with a velocity of √(2gh) downwards. Therefore, the velocity of sound waves relative to the source is:
vs = v ± √(2gh)
Substituting this in the above equation and solving for h, we get:
h = (v²/2g) [(f2/f1)² - 1]
Substituting the given values, we get:
h = (330²/2×9.81) [(120/100)² - 1] = 308 m
Therefore, the height of the building is 308 m.
Answer: Option B. 308 m
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Community Answer
A man jumps from a building with a source of sound. When he reaches ha...
We can find the speed corresponding to the apparent frequency and then use that to find the height of the building.
120 = 100(330)/(330-v) v = 330 – 3300/12 = 55m/s.
Using, v2 = 2gh, we can find the height covered by the man. The double of this value will be the height of the building as he is mid-way.
552 = 2*9.81*h h = 154m Height of building = 2h = 308m.
120 = 100(330)/(330-v) v = 330 – 3300/12 = 55m/s.
Using, v2 = 2gh, we can find the height covered by the man. The double of this value will be the height of the building as he is mid-way.
552 = 2*9.81*h h = 154m Height of building = 2h = 308m.
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A man jumps from a building with a source of sound. When he reaches halfway down, he starts the siren of frequency 100Hz. A person standing below him on the ground hears the first sound to be of frequency 120Hz. What is the height of the building? Speed of sound = 330m/s. Take g=9.81m/s2.a)154mb)308mc)77md)500mCorrect answer is option 'B'. Can you explain this answer?
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A man jumps from a building with a source of sound. When he reaches halfway down, he starts the siren of frequency 100Hz. A person standing below him on the ground hears the first sound to be of frequency 120Hz. What is the height of the building? Speed of sound = 330m/s. Take g=9.81m/s2.a)154mb)308mc)77md)500mCorrect answer is option 'B'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A man jumps from a building with a source of sound. When he reaches halfway down, he starts the siren of frequency 100Hz. A person standing below him on the ground hears the first sound to be of frequency 120Hz. What is the height of the building? Speed of sound = 330m/s. Take g=9.81m/s2.a)154mb)308mc)77md)500mCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man jumps from a building with a source of sound. When he reaches halfway down, he starts the siren of frequency 100Hz. A person standing below him on the ground hears the first sound to be of frequency 120Hz. What is the height of the building? Speed of sound = 330m/s. Take g=9.81m/s2.a)154mb)308mc)77md)500mCorrect answer is option 'B'. Can you explain this answer?.
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